Best Known (168, 168+∞, s)-Nets in Base 4
(168, 168+∞, 200)-Net over F4 — Constructive and digital
Digital (168, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (168, 199)-sequence over F4, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
(168, 168+∞, 215)-Net over F4 — Digital
Digital (168, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (168, 214)-sequence over F4, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 148 and N(F) ≥ 215, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
(168, 168+∞, 521)-Net in Base 4 — Upper bound on s
There is no (168, m, 522)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (168, 2604, 522)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42604, 522, S4, 5, 2436), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 197558 779768 367635 583796 784753 961660 352566 357643 772853 597639 729273 130944 831067 241107 747935 942704 632908 551213 320440 767978 344897 447546 942328 637591 700838 877203 920389 785359 587915 675457 671106 520714 581061 619052 453899 174794 547309 349614 623286 218855 473724 875072 977911 200777 155382 593683 515590 065341 174852 211509 726426 327648 732178 066663 019756 596599 880759 795017 773397 832038 494113 927756 941057 147469 939030 347833 987446 104844 696043 925509 111565 993685 189374 087566 024005 963835 673789 206555 661827 763073 212170 781404 223178 794028 994402 658935 987711 032930 253759 454140 062714 834715 303098 560153 179663 173032 833836 301742 366279 732966 327155 922887 846460 206609 883606 284681 984533 637773 463221 690342 677624 743021 938828 233032 445010 178211 548972 598469 833509 223363 539796 043069 870257 358326 176453 268893 115857 289944 790523 179832 416411 186795 206173 484127 098907 008838 350604 628274 290890 423252 335510 889473 645941 211935 338312 416836 793093 940234 165147 650773 052328 064971 774956 883728 990365 556101 635308 745873 809149 850769 174534 794257 718758 892730 609993 635803 546628 494325 097824 815647 198130 417513 492880 586450 013766 148311 505133 508990 519679 240548 172290 889879 197767 031697 783695 594000 881470 355690 833428 951904 183241 737573 168208 069552 293509 983285 229216 405760 449832 080654 324431 047820 552312 812294 089657 572283 834597 999975 180132 546975 077320 617767 672458 534177 182872 747323 280242 972778 789818 112459 087301 179627 412442 267221 313806 302506 509753 333892 676747 014074 624218 397908 824592 118065 687885 673739 528142 737131 500588 872472 757074 150787 189249 219387 448216 990196 467298 397568 999054 571978 287833 437620 337922 582395 605211 182670 135810 700751 460349 427060 824237 670400 / 2437 > 42604 [i]
- extracting embedded OOA [i] would yield OOA(42604, 522, S4, 5, 2436), but